# Math Help - Series problems

1. ## Series problems

I have two problems: 1. I have to give examples of series Xk and Yk which are conditionally convergent and Xk < ((-1)^(k+1))/k and (-1)^(k+1)Yk < 1/k. What could them be? 2. We know that Sn = ΣXk (k=1 -> n), An = Sn/n = 1/n*ΣXk (k=1 -> n) and limXn= b∈ℝ as n -> ∞. What can be said about limAn as n -> ∞?

3. Both $|X_k|$ and $|Y_k|$ must be less than $\frac{1}{k}$ and be conditionally convergent. The easiest example of this is $X_k = \frac{(-1)^k}{ck}$ where c is a positive real number greater than 1.